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How to program gravity for planets?

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I want to make a 2-D platformer/puzzle game involving multiple small "planets" similar to Super Mario Galaxy. How would I go about programming gravity for these planets so that the closest large planet pulls the player towards it (like in real life)?

Also, I'm running into a bit of trouble programming the movement script for this as well. So if anyone knows how to move the player in a circular motion, that'd be great.

foreach planet
gravitational_constant = 100 <-- make something up here until you get pleasing results
distance_squared = (planet.position - player.position).sqrmagnitude
// get the masses - note that the planet mass needs to be much larger than the player mass
// and make sure these values are set on the rigidbody so the Unity physics will act correctly
// when the force is applied
mass1 = planet.mass = 1000 <-- mess around with these until you get pleasing results
mass2 = player.mass = 1 <-- this can probably always stay 1 for the player
force = gravitational_constant * ((mass1 * mass2) / distance_squared);
// e.g. plugging in the values...
// force = 100 * ((1000 * 1) / distance_squared)
// apply the force from the player toward the planet
force_direction = (planet.position - player.position).normalized;
force_vector = force_direction * force;
// TODO : use AddForce or whatever to apply force_vector to the player's rigidbody
// you end up adding each force vector to the player so it will move toward the
// strongest/closest/most_massive planet.

Basically the force is the object masses multiplied together, then scaled by the distance between the bodies, then adjusted by the gravitational constant. You can change the mass of each planet based on its sized to make larger planets have a larger attraction.

Thanks much! However, do you know how I would go about applying a normal force to the player when they are on the "planet" so that they don't go straight through the planet?

I currently am using a rigidbody on my player, and using AddForce to apply the gravity. In a different script, I have a Raycast casting towards the center of the planet, but this isn't working:`rigidbody.AddForce(hit.normal*Mars.GetComponent(Gravity).force)`. Where I have your gravity script saved as "Gravity" and applied to Mars (a previously declared variable of my planet). Once the player reaches the surface of the planet, it will slow the player down, but not enough to completely stop it. If I lower the gravity, the player just bounces up and down on the surface.

you can add a constant force pulling the player to the centre of the planet, and if the player is a certain distance from the planet, the constant force can be turned off or reduced relative to distance, like that he will always be attracted to the centre of the planet and if he goes far enough away he will be in free space. it also means that if you freefall in the planet's atmosphere you will accelerate into the ground and if you jump in the air it will be the same as gravity, except towards the centre.

you can add a constant force pulling the player to the centre of the planet, and if the player is a certain distance from the planet, the constant force can be turned off or reduced relative to distance, like that he will always be attracted to the centre of the planet and if he goes far enough away he will be in free space. it also means that if you freefall in the planet's atmosphere you will accelerate into the ground and if you jump in the air it will be the same as gravity, except towards the centre.